solving economic dispatch problems by using grey wolf...

Solving Economic Dispatch Problems ByUsing Grey Wolf Optimization Technique

AlaaSiddig Ali Alaa.FSheta

Faculty of Graduate StudiesComputer Science

DepartmentFaculty of Computer Science and Information

Technology Taif UniversitySudan University of Science and Technology Taif , saudiarabia

Email: [email protected]:

[email protected]

ABSTRACT

The Economic dispatch (ED) is of vital importance since itdoesn’t only reduces the operation cost of the generation utilitybut also helps in conserving fast dwindling energy resources.They are many researches that have been developer to minimizefuel cost based on swarm intelligence also.The SwarmIntelligence algorithms preserve information about the searchspace over the course of iteration, whereas evolutionaryalgorithms (EA) discard the information of the previousgenerations. SI algorithms have fewer operators compared toevolutionary approaches. This paper discussed some issues ofSwarm Intelligence techniques for a new meta-heuristic andproduct Grey Wolf Optimizer (GWO) inspired by greywolves(Canis lupus). The efficiency and effectiveness of theproposed technique is benchmarked for different test casesconsisting of three, six for generating units with high non-linearity. The results of the GWO compared with that of otherintelligence optimization algorithms in terms of operating costof generators and power generation. Wide contrasting simulationresults are observed with the other swarm, nature and bioinspired algorithms.GWO results in minimum operating cost,minimum standard deviation among best, mean and worstsolution showing good exportability, fast convergence withiteration leads to robustness and good solution quality.

Index Terms

IJISET - International Journal of Innovative Science, Engineering & Technology, Vol. 4 Issue 9, September 2017 ISSN (Online) 2348 – 7968 | Impact Factor (2016) – 5.264

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Economic dispatch (ED); Grey Wolf Optimization (GWO).

1. INTRODUCTION

The main aim of power system supply utility has been identifiedas to provide the smooth power generation system to theconsumers. It will be ensured that the electrical power isgenerated with minimum cost. That is mean to achieve aneconomic operation of the power system; the total demand mustbe appropriately shared among the units. This will minimize thetotal generation cost for the power system with the voltage levelmaintained at the safe operating limits. Economic dispatcherdefined as the process of allocating generation levels to thegenerating units in the mix so that the system load is fullysupplied in the most economical way. The method of economicdispatch for generating units at different loads must have totalfuel cost at the minimum point.Meta-heuristic classified into three main classes areevolutionary, physics-based and swarm intelligence(SI). SIincludes Particle Swarm Optimization (PSO), Artificial BeeColony (ABC), Cuckoo Search (CS) and Firefly Algorithm (FA)techniques. Many of these techniques are inspired by huntingand search behaviors. To the best of our knowledge, however, SIdoes not support grey wolves known by pack hunting; thismotivated our attempt to mathematically model the socialbehavior of grey wolves in solving benchmark and realproblem.Grey wolf is a new population based method which isintroduced in 2014 by Mirjalili et al. GWO algorithm is inspiredby grey wolves. The technique follows the social hierarchy andhunting path of grey wolves

Inspiration: The GWO are mostly preferred to live in a pack.Our group size is 5-12 on average. The particular interest is thatthey have a very strict social dominant hierarchy as shown inFig. 1.


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Fig 1:Hierarchy of grey wolf

The follow-up of grey wolf hunting are:• Tracking, chasing, and approaching the victim.

• Pursuing, encircling, and harassing the victim until it stopsmoving.

• Attack towards the victim.

These steps are shown in Fig 2.

Fig 2.Hunting behaviour of grey wolves: (A) chasing, approaching, and tracking prey (B, C, D) pursuiting,harassing, and encircling(E) stationary situation and attack

In this paper we take three units and test power generation byapplying newmeta-heuristictechnique calledGrey WolfOptimization (GWO) for solve the problem of economic loaddispatch by minimize fuel cost for unit generation, The GWO isinspired by grey wolves(Canis lupus). The GWO algorithmmimics the leadership hierarchy and hunting mechanism ofgreywolves in nature. Four levels of grey wolves such as alpha,beta, delta, and omega that work in a hierarchyare employed forsimulatingthe leadership hierarchy. In addition, there are three


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main steps of hunting, searching for prey, encirclingprey, andattacking prey, are implemented.

2. METHODS

2.1. PROBLEM FORMULATIONThe ED problem may be stated as to reduce the fuel cost ofgenerator units with several constraints. Mathematically, it mayexpress as:A) Economic dispatch problem (Minimization of FuelCost)Fuel cost model

Subjected to following constraints

Where,

,

,

This equation is about how extract the minimal fuel cost bychoosing the best power generation which we take average ofminimal power generation and maximum power generation toreach into best generation and minimal fuel cost,.

2.2. Grey Wolf Optimization

2.2.1.Mathematical model and algorithm

Social hierarchy: For modeling the social hierarchy of wolvesuntil designing GWO, the fittest solution is considered as thealpha (α). Accordingly, the second and third best solutions arenamed beta (β) and delta (ᵟ) respectively. The rest of the


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candidate solutions are considered to be omega (ω). The wwolves follow these three wolves.

Encircling prey: Next, for designing encircling behavior, someequations are considered:D= (C. XP(t)-X(t))X (t+1) =Xp(t)-A.DWhere(t) is the current iteration, A and C are coefficientvectors, Xp(t) represents the position vector of the victim. Thevectors A and C can be calculated as below:X=2.a.r1-a

C=2.r2Where component of a are linearly decreased from 2 to 0 overthe course of iterations and r1 and r2 are random vectors in therange [0, 1]

Hunting: In GWO, the first three best solutions obtained arestored so far and push the other search agents (including theomegas) to update their positions due to the position of the bestsearch agents. The following equations are modeled.

The final position would be in a random position within a circlewhich is defined by the positions of alpha, beta, and delta in thesearch space.

3. Results and Discuss

3.1. Algorithms Numerical SettingsGWO: Population size =50, coefficient a=[0-2],Iterations=5003.2.TheMetrics of Generation that we used in explain are asfollows:


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MW: Mega Watt of Power GenerationPGmin(MW): Minimum Power GenerationPGmax(MW): Maximum Power Generation

3.3. Approach of Power Demand Formulation UsingGWOVariablesPower Generation (PG) and cost coefficients (a,b,c) of unitswith fitness function as fuel cost, quadratic in nature and valvepoint effect .ConstraintsEquality Constraints: Power Generation-PowerDemand=0(PG=Pd)In-Equality Constraints: Power Generation should be betweenminimum and maximum limit of power generation.Stopping CriteriaIt is the maximum number of iteration for optimum solution.3.4. Test System DataTo check the effectiveness of GWO for ED problems, twodifferent case studies are taken.

Table 1: Three generating unit systemdata

Unit a($/MW2 ) b($/MW) c($ ) PGmin(MW) PGmax(MW)

1 0.008 7 200 10 85

2 0.009 6.3 180 10 80

3 0.007 6.8 140 10 70

Table 2: Six generating unit system dataUnit a($/MW2) b($/MW) c($ ) PGmin(MW) PGmax(MW)

1 0.007 7 240 100 500

2 0.005 10 200 50 200

3 0.009 8.5 220 80 3004 0.009 11 200 50 1505 0.0080 10.5 220 50 200

6 0.0075 12 120 50 120


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3.5.Numerical ResultThe proposed technique is tested on different benchmarks forsimulation. Comparative analysis is demonstrated with otheroptimization techniques

Table 3: Results comparison with other techniques and cost (Power Demand-150 MW)Parameters GWO CS ABC FA

PG1(MW) 550.55 33.490 33.049 32.729

PG2(MW) 481.725 64.116 61.764 63.843

PG3(MW) 423.2 55.126 57.872 56.151

Cost($/hr) 1455.475 1600.46 1600.51 1600.47

Fig 3: Comparison of Total cost of GWO with othertechniques on three units

Table 4: Result comparison of different technique costfor six units

Techniques GWO CS ABC FA PSO SFL BFO HSCost($/hr) 7804.603125 8356.06 8372.27 8388.45 8401.45 8419.78 8428.69 8398.06


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Fig 4: Comparison of Total cost of GWO with othertechniques on six units

CONCLUSIONIn this paper we discuss the Economic dispatch (ED) aims atdistributing the load demand between all of various generationunits in an electrical system such that the total cost of generationis very minimum. We were used some equations in SwarmIntelligence techniques for a new meta-heuristic called GreyWolf Optimizer (GWO) inspired by grey wolves(Canis lupus) tosolved problem of ED. The GWO algorithm mimics theleadership hierarchy and hunting mechanism of greywolves innature.It proposes an effective and reliable Grey WolfOptimization (GWO) technique for the economic load dispatchproblem. The efficiency and effectiveness of the proposedtechnique is benchmarked for different test cases consisting ofthree, six for generating units with high non-linearity. Theresults of the GWO compared with that of other intelligenceoptimization algorithms in terms of operating cost of generatorsand power generation. Wide contrasting simulation results areobserved with the other swarm, nature and bio inspiredalgorithms.GWO results in minimum operating cost, minimumstandard deviation among best, mean and worst solutionshowing good exportability, fast convergence with iterationleads to robustness and good solution quality.


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[9]Majumdar, Kingsuk, Provas Kumar Roy, and SubrataBanerjee. "Available Transfer Capacity evaluation throughBBO and GWO algorithms." Foundations and Frontiers inComputer, Communication and Electrical Engineering:Proceedings of 3rd International Conference C2E2,Mankundu, West Bengal, India, 15th-16th January, 2016..CRC Press, 2016.

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